Question

What is the probability of getting $2$ heads in $3$ tosses?

Answer 1

Find the probability of getting $2$ heads in $3$ tosses:

The probability of an event is,

$\mathbf{P}\left(E\right)\mathbf{}\mathbf{=}\mathbf{}\frac{\mathbf{Number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{favourable}\mathbf{}\mathbf{outcomes}}{\mathbf{Total}\mathbf{}\mathbf{number}\mathbf{}\mathbf{of}\mathbf{}\mathbf{outcomes}}$

When a coin is tossed $3$ times, the possible outcomes are:

$TTT,TTH,THT,THH,HHH,HHT,HTH,HTT$

The total number of outcomes $=8$

Let $E$ be the event of getting $2$ heads.

$E=\left\{THH,HHT,HTH\right\}$

The number of a favorable outcomes $=3$

Then, the probability of getting $2$ heads is,

$P\left(E\right)=\frac{3}{8}$

Hence, the probability of getting $2$ heads in $3$ tosses is $\frac{3}{8}$.